Babar Z. From Classical to Quantum Coding 2026

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Babar Z. From Classical to Quantum Coding 2026

Textbook in PDF format An expert discussion of the potential evolution of quantum codes In From Classical to Quantum Coding, a team of distinguished researchers deliver a seamless book on the subject of quantum error correction codes (QECC) designed for mitigating the environment-induced decoherence imposed on quantum computing and communications. Part I provides a gentle introduction to the rudimentary principles, paving the way for readers familiar with classical coding to quantum coding, including the associated quantum and classical coding basics. Part II is dedicated to the family of near-term quantum codes, which do not require a high number of qubits and, hence, are suitable for near-term intermediate scale (NISC) quantum computers, for example. Finally, Part III elaborates on the design of a suite of sophisticated long-term quantum coding solutions, when having a relatively high number of qubits becomes realistic, as quantum technology matures. A range of adaptive-rate quantum codes are also conceived for practical scenarios of time-variant depolarizing probability. The book incorporates several advanced topics, including the universal decoding of arbitrary linear codes, iterative short turbo block codes, turbo convolutional codes, and the family of low-density parity check codes. The powerful design tool of extrinsic information transfer charts plays a central role in the associated near-hashing-bound designs. Readers will also find: An easy-reading introduction to quantum information processing and quantum coding An evolutionary portrayal of the classical to quantum coding paradigm Practical discussions of near-term quantum topological error correction codes and how they protect quantum gates from decoherence Detailed treatments of syndrome-based decoding of diverse quantum turbo codes and quantum low-density parity check codes From Classical to Quantum Coding will benefit doctoral students, and industrial and academic researchers wishing to expand their expertise from the classical to the quantum field of signal processing, computing and communications. Contents: Preface Acknowledgments Part I: From Classical to Quantum Codes Part II: Near-term Quantum Codes Part III: Advanced Quantum Codes Appendix A: Construction of Syndrome Former Appendix B: Simulation of QLDPC Decoding Glossary References Subject Index Author Index About the Author Zunaira Babar is a Senior Algorithm Engineer at VIAVI Solutions Inc. Daryus Chandra is a Senior Quantum Error Correction Researcher at Photonic Inc. Soon Xin Ng, PhD, is a Full Professor of Telecommunications at the University of Southampton, UK. Lajos Hanzo is a Fellow of the Royal Academy of Engineering and a Foreign Member of the Hungarian Academy of Sciences. Table of Contents About the Authors xiii List of Acronyms xv Preface xvii Acknowledgments xix Part I From Classical to Quantum Codes 1 Introduction Motivation Historical Overview Outline of the Book Preliminaries on Quantum Information Introduction A Brief Review of Quantum Information Quantum Information Processing Quantum Decoherence No-cloning Theorem Quantum Entanglement Quantum Channels Summary and Conclusions From Classical to Quantum Coding Introduction A Brief Review of Classical Syndrome-based Decoding A Brief Review of Quantum Stabilizer Codes Protecting a Single Qubit: Design Examples Summary and Conclusions Revisiting Classical Syndrome Decoding Introduction Look-up Table-based Syndrome Decoding Trellis-based Syndrome Decoding Block Syndrome Decoding Results and Discussion Summary and Conclusions Near-capacity Codes for Entanglement-aided Classical Communication Introduction Review of the SD Coding Protocol Entanglement-assisted Classical Capacity Bit-based Code Structure Near-capacity Design Results and Discussion Symbol-based Code Structure I Results and Discussion II Summary and Conclusion Part II Near-term Quantum Codes Quantum Coding Bounds and a Closed-form Approximation of the Minimum Distance Versus Quantum Coding Rate Introduction 111 On Classical to Quantum Coding Bounds Quantum Coding Bounds in the Asymptotical Limit Quantum Coding Bounds on Finite-length Codes The Bounds on Entanglement-assisted Quantum Stabilizer Codes Summary and Conclusions Quantum Topological Error Correction Codes: The Classical-to-quantum Isomorphism Perspective Introduction Classical Topological Error Correction Codes: Design Examples Quantum Topological Error Correction Codes: Design Examples Performance of Quantum Topological Error Correction Codes Summary and Conclusions 151 Protecting Quantum Gates Using Quantum Topological Error Correction Codes Introduction Protecting Transversal Gates Design Examples Error Model Simulation Results and Performance Analysis Conclusions and Future Research Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork Introduction Decoding Classical FEC Codes via Guesswork Quantum Stabilizer Codes Decoding Quantum Stabilizer Codes Results and Discussion Conclusions and Future Work Part III Advanced Quantum Codes Revisiting the Classical to Quantum Coding Evolution Introduction Review of Classical Linear Block Codes Quantum Stabilizer Codes Quantum Convolutional Codes Entanglement-assisted Quantum Codes Summary and Conclusions EXIT-chart Aided Near-hashing-bound Concatenated Quantum Codes Introduction Design Objectives Circuit-based Representation of Stabilizer Codes Revisiting Concatenated Quantum Codes EXIT Chart Aided Quantum Code Design Results and Discussion I Quantum Irregular Convolutional Codes Results and Discussion II Summary and Conclusions Near-hashing-bound Quantum Turbo Short-block Codes Introduction to Iterative Decoding Quantum Short-block Codes Quantum Turbo Code Design Using QSBCs Results and Analysis Conclusions and Future Research EXIT-chart-aided Design of Irregular Multiple-rate Quantum Turbo Block Codes Introduction Quantum Short-block Codes Quantum Turbo Short-block Codes EXIT-chart Analysis Multiple-rate Quantum Turbo Short-block Codes Conclusions Quantum Low-density Parity Check Codes Introduction Quantum LDPC Code Designs Iterative Decoding of Quantum LDPC Codes High-rate QLDPC Codes from Row-circulant Classical LDPCs Results and Discussions I Modified Non-binary Decoding Reweighted BP for Graphs Exhibiting Cycles Results and Discussions II Summary and Conclusions Summary and Future Research Summary Future Research A Construction of Syndrome Former A.1 Convolutional Codes A.2 Turbo Trellis Coded Modulation B Simulation of QLDPC Decoding Glossary References Subject Index Author Index